1. You decide to test a friend for ESP using a standard deck of 52 playing cards. Such a deck contains 13 spades, 13 hearts, 13 diamonds, and 13 clubs. You shuffle the deck, select a card at random, and ask your friend to tell you whether the card is a spade, heart, diamond, or club. After the guess you return the card to the deck, shuffle the cards, and repeat the above. You do this a total of 100 times. Let X be the number of correct guesses by your friend in the 100 trials. The standard deviation of X is
A. 0.433.
B. 4.33.
C. 18.75.
2. You decide to test a friend for ESP using a standard deck of 52 playing cards. Such a deck contains 13 spades, 13 hearts, 13 diamonds, and 13 clubs. You shuffle the deck, select a card at random, and ask your friend to tell you whether the card is a spade, heart, diamond, or club. After the guess you return the card to the deck, shuffle the cards, and repeat the above. You do this a total of 100 times. Let X be the number of correct guesses by your friend in the 100 trials. What is the probability that X 30 if your friend is just guessing? Use the Normal approximation with the continuity correction.
A. 0.1492
B. 0.30
C. 0.8508
3. Which of the following might be reasonably modeled by the binomial distribution?
A. The number of customers that enter a store in a one-hour period, assuming customers enter independently.
B. The number of questions you get correct on a 100-question multiple choice exam in which each question has only four possible answers. Assume you have studied extensively for the test.
C. Neither choice is correct.